Preimage Attacks on CellHash, SubHash and Strengthened Versions of CellHash and SubHash

CellHash [3] and SubHash [4] were suggested by J. Daemen, R. Govaerts and J. Vandewalle in 1991 and 1992. SubHash is an improved version from CellHash. They have 257-bit internal state and 256-bit hash output. In this paper, we show a preimage attack on CellHash (SubHash) with the complexity 2 and the memory 2 for any t (with the complexity about 2 and the memory size 2). Even though we modify them in a famous way, we show that we can find a preimage on the modified CellHash (the modified SubHash) with the complexity 2 and the memory size 2 (with the complexity about 2 and the memory size 2).